**2.3 Drying kinetics and modelling**

The *drying kinetics* is used to describe the combined macroscopic and microscopic mechanisms of heat and mass transfer during *drying*, and it is affected by *drying* conditions, types of *dryer* and characteristics of materials to be *dried*. Studying drying kinetics is a means to choose appropriate drying methods and to control the processes of drying. It is also important for engineering and process optimization. Drying kinetics is used to show removal of moisture from products, and it has to do with process variables, and hence, a better understanding of drying rate will help in developing a drying rate model [78]. There are three drying models, namely, theoretical, semi-theoretical and empirical according to Khazae and Daneshmandi [79]. Theoretical models dealt with internal resistance in transfer of moisture, while semi-theoretical and empirical models worked on external resistance in the transfer of moisture between air and products [80]. Empirical model's main shortcoming is that it does not consider the basics of drying process but explains only the drying curve for drying conditions but not the processes that occur during drying [81]. Examples of semi-theoretical models are the Lewis model, Henderson and Pabis model, Logarithmic model, Page model, etc.

The theoretical model that is commonly used in drying rate is Fick's second law of diffusion. Theoretical models have been found to be inadequate, tend to generate erroneous results and are complex for practical applications. Therefore, in food drying semi-theoretical models have been developed as a better model to fit the drying data of banana fruits to be dried [82]. In the case of the Henderson and Pabis model, it was first used for model drying of corn. But due to inaccuracy and high degree of temperature difference between kernel and air, the model could not be fitted during the first 1 or 2 h of drying banana [83]. The Lewis model is a special case of the Henderson and Pabis model [84]. However, the model has been found to be inaccurate because it overestimates the first period and underestimates the last period of drying. But, semi-theoretical models have been found to be the simplified general series solutions of Fick's second law (**Table 2**).

### *2.3.1 Effect of air temperature and air velocity on drying kinetics*

In drying kinetics, air temperature is one of the major factors influencing the drying kinetics during dehydration. Krokida et al. [83] reported that the drying constant, equilibrium moisture content and moisture diffusivity increase as the temperature increases. Tzempelikos et al. [85] in their experiment on the time of drying banana fruits found that the drying was influenced by the air temperatures and air velocities used for drying. They discovered that drying time was reduced by 30% with increase in the air velocity at a temperature of 60°C, while 54% reduction in drying time was observed when temperature was increased from 40 to 60°C at an air velocity of 2 m/s.

#### *2.3.2 Effect of shape on drying kinetics*

Borges et al. [86] studied the influence of shape on the drying kinetics of banana. They reported that the shape of produce has positive influence drying kinetics and that the drying rate was significantly higher with disk-shaped Dagua banana as compared to the cylindrical shaped banana. They also reported that shape of produce has positive influence on drying temperature of Parta banana and observed that the effect of blanching in Parta banana could been seen when dried at 40°C as compared to shape; the air velocity and air temperature were found to have a more profound effect on the drying time. They also observed that the drying square slices were lower than the cylindrical samples.


*Key terms: T—drying time (s); a, b, c, g, n—dimensionless constants for drying; k, k1, ko—drying velocity constants; exp—exponential; MR—moisture ratio; L—thickness of the material; R—correlation coefficient.*

**73**

*Banana Drying Kinetics*

*monocytogenes* [92].

*2.3.4 Effect of relative humidity*

*2.3.5 Mass transfer parameters*

*2.3.6 Effective moisture diffusivity*

extend the banana product shelf life.

attributed to the initial moisture content of the sample.

diffusivity and activation energy dependence [94].

*2.3.3 Effect of pretreatment*

*DOI: http://dx.doi.org/10.5772/intechopen.84669*

Pretreatment is done in banana slices before drying has been found to reduce the drying time, to improve taste and structure, to preserve flavour and to maintain the nutrition of banana. Pretreatment reduces the initial moisture content and modifies

Relative humidity has serious effect on drying rate and drying kinetic of banana fruits. Misha et al. [93] worked on the effect of humidity and temperature in the drying kinetics. They used drying temperature (45, 50 and 55°C) and relative humidity (10, 20 and 30%) variations at an air velocity of 1.0 m/s. They found that two-term model described the drying kinetics more accurately and then the rest of the models used in the experiment. They also found that the drying time was reduced as the temperature increased at constant air humidity. They observed that relative humidity of the air had an insignificant effect on the drying curve; this was

Drying process is used to prolong the storage or shelf life of banana products without changing the quality, structure and chemical properties. This is critically needed for quality of banana products and availability. The efficient and effective drying process could be obtained through an effective use of time, energy and cost [94]. This could also be seen in through speed and timely removal of moisture during the drying process. It has been established that moisture removal depends on the drying method and this will affect the technique of moisture movement towards evaporation for the drying process. Moisture movement is also effective moisture

Effective moisture diffusivity is defined as movement of moisture in banana products and is drying rate related [94, 95]. The difference between effective moisture diffusivity and drying rate is that effective moisture diffusivity is related to moisture velocity within the material, while the drying rate is the moisture vapourizing rate to air and depends directly on the pressure gradient that exists between material and the air due to a temperature gradient [94]. Effective moisture diffusivity is the parameter used to determine the drying rate of banana products and an indicator to determine an appropriate drying method that could be used to

Also, according to Omolola et al. [87], effective moisture diffusivity is said to be a function of material moisture content and temperature, as well as of the material

the tissues of the banana fruits which help to accelerate the drying rate [87]. Common pretreatments applied to fruits prior to drying operation include blanching, lemon juice, ascorbic acid, sulfuring, honey dip, salt solution and osmotic pretreatment, ethyloleate, NaOH, olive oil, skin puncturing and K2CO3 [88–91, 92]. Studies have shown that pretreating with an acidic solution or sodium metabisulfite dip also enhances the destruction of potentially harmful bacteria during drying, including *Escherichia coli* O157:H7, *Salmonella* spp. and *Listeria* 

#### **Table 2.**

*Mathematical models used in banana drying kinetics.*

## *2.3.3 Effect of pretreatment*

*Banana Nutrition - Function and Processing Kinetics*

general series solutions of Fick's second law (**Table 2**).

air velocity of 2 m/s.

*2.3.2 Effect of shape on drying kinetics*

square slices were lower than the cylindrical samples.

Simplified Fick's diffusion equation MR = a exp[−c(t/L2

Modified page II MR = exp(exp(−c(t/L2

Simplified Fick's diffusion MR = a exp(−c(t/L2

Modified page MR = exp[−(kt)n

*Mathematical models used in banana drying kinetics.*

*2.3.1 Effect of air temperature and air velocity on drying kinetics*

erroneous results and are complex for practical applications. Therefore, in food drying semi-theoretical models have been developed as a better model to fit the drying data of banana fruits to be dried [82]. In the case of the Henderson and Pabis model, it was first used for model drying of corn. But due to inaccuracy and high degree of temperature difference between kernel and air, the model could not be fitted during the first 1 or 2 h of drying banana [83]. The Lewis model is a special case of the Henderson and Pabis model [84]. However, the model has been found to be inaccurate because it overestimates the first period and underestimates the last period of drying. But, semi-theoretical models have been found to be the simplified

In drying kinetics, air temperature is one of the major factors influencing the drying kinetics during dehydration. Krokida et al. [83] reported that the drying constant, equilibrium moisture content and moisture diffusivity increase as the temperature increases. Tzempelikos et al. [85] in their experiment on the time of drying banana fruits found that the drying was influenced by the air temperatures and air velocities used for drying. They discovered that drying time was reduced by 30% with increase in the air velocity at a temperature of 60°C, while 54% reduction in drying time was observed when temperature was increased from 40 to 60°C at an

Borges et al. [86] studied the influence of shape on the drying kinetics of banana. They reported that the shape of produce has positive influence drying kinetics and that the drying rate was significantly higher with disk-shaped Dagua banana as compared to the cylindrical shaped banana. They also reported that shape of produce has positive influence on drying temperature of Parta banana and observed that the effect of blanching in Parta banana could been seen when dried at 40°C as compared to shape; the air velocity and air temperature were found to have a more profound effect on the drying time. They also observed that the drying

**Models for drying Formulas Reference** Two term MR = a exp(−k0 t) + b exp(−k1 t) [81]

Henderson and Pabis MR = a exp(−kt) [83]

Lewis model MR = exp(−kt) [85]

Page model MR = exp(−ktn) [62]

*exp—exponential; MR—moisture ratio; L—thickness of the material; R—correlation coefficient.*

*Key terms: T—drying time (s); a, b, c, g, n—dimensionless constants for drying; k, k1, ko—drying velocity constants;* 

)] [82]

)n) [60]

)) [60]

] [63]

**72**

**Table 2.**

Pretreatment is done in banana slices before drying has been found to reduce the drying time, to improve taste and structure, to preserve flavour and to maintain the nutrition of banana. Pretreatment reduces the initial moisture content and modifies the tissues of the banana fruits which help to accelerate the drying rate [87].

Common pretreatments applied to fruits prior to drying operation include blanching, lemon juice, ascorbic acid, sulfuring, honey dip, salt solution and osmotic pretreatment, ethyloleate, NaOH, olive oil, skin puncturing and K2CO3 [88–91, 92]. Studies have shown that pretreating with an acidic solution or sodium metabisulfite dip also enhances the destruction of potentially harmful bacteria during drying, including *Escherichia coli* O157:H7, *Salmonella* spp. and *Listeria monocytogenes* [92].
